Solve 5n-2/12-3(n-3)/8

$$\frac { 5 n - 2 } { 12 } - \frac { 3 ( n - 3 ) } { 8 }$$

Evaluate

$$\frac{n+23}{24}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 8 is 24. Multiply \frac{5n-2}{12} times \frac{2}{2}. Multiply \frac{3\left(n-3\right)}{8} times \frac{3}{3}.

$$\frac{2\left(5n-2\right)}{24}-\frac{3\times 3\left(n-3\right)}{24}$$

Since \frac{2\left(5n-2\right)}{24} and \frac{3\times 3\left(n-3\right)}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(5n-2\right)-3\times 3\left(n-3\right)}{24}$$

Do the multiplications in 2\left(5n-2\right)-3\times 3\left(n-3\right).

$$\frac{10n-4-9n+27}{24}$$

Combine like terms in 10n-4-9n+27.

$$\frac{n+23}{24}$$

Expand

$$\frac{n+23}{24}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 8 is 24. Multiply \frac{5n-2}{12} times \frac{2}{2}. Multiply \frac{3\left(n-3\right)}{8} times \frac{3}{3}.

$$\frac{2\left(5n-2\right)}{24}-\frac{3\times 3\left(n-3\right)}{24}$$

Since \frac{2\left(5n-2\right)}{24} and \frac{3\times 3\left(n-3\right)}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(5n-2\right)-3\times 3\left(n-3\right)}{24}$$

Do the multiplications in 2\left(5n-2\right)-3\times 3\left(n-3\right).

$$\frac{10n-4-9n+27}{24}$$

Combine like terms in 10n-4-9n+27.

$$\frac{n+23}{24}$$